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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [74] had the largest ratio of [16]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 4 3 1.00 12 0.250
2 A 4 3 1.00 12 0.250
3 A 4 3 1.00 12 0.250
4 A 4 3 1.00 12 0.250
5 A 3 3 1.00 10 0.300
6 A 3 2 1.00 8 0.250
7 A 3 2 1.00 12 0.167
8 A 5 5 1.00 12 0.417
9 A 3 3 1.00 12 0.250
10 A 4 3 1.00 12 0.250
11 A 4 3 1.00 12 0.250
12 A 4 3 1.00 12 0.250
13 A 16 7 1.00 14 0.500
14 A 14 9 1.00 14 0.643
15 A 11 7 1.00 14 0.500
16 A 9 8 1.00 14 0.571
17 A 6 5 1.00 12 0.417
18 A 5 5 1.00 10 0.500
19 A 6 5 1.00 14 0.357
20 A 4 4 1.00 14 0.286
21 A 8 7 1.00 14 0.500
22 A 8 7 1.00 14 0.500
23 A 13 8 1.00 14 0.571
24 A 33 11 1.00 14 0.786
25 A 24 11 1.00 14 0.786
26 A 18 10 1.00 14 0.714
27 A 12 9 1.00 14 0.643
28 A 8 8 1.00 12 0.667
29 A 5 6 1.00 10 0.600
30 A 8 6 1.00 14 0.429
31 A 5 6 1.00 14 0.429
32 A 7 6 1.00 14 0.429
33 A 14 11 1.00 14 0.786
34 A 16 8 1.00 14 0.571
35 A 0 0 0.00 0 0.000
36 A 0 0 0.00 0 0.000
37 A 0 0 0.00 0 0.000
38 A 0 0 0.00 0 0.000
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 0 0 0.00 0 0.000
42 A 0 0 0.00 0 0.000
43 A 0 0 0.00 0 0.000
44 A 0 0 0.00 0 0.000
45 A 0 0 0.00 0 0.000
46 A 0 0 0.00 0 0.000
47 A 0 0 0.00 0 0.000
48 A 0 0 0.00 0 0.000
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 0 0 0.00 0 0.000
52 A 0 0 0.00 0 0.000
53 A 12 9 1.00 8 1.125
54 A 0 0 0.00 0 0.000
55 A 0 0 0.00 0 0.000
56 A 2 2 1.00 14 0.143
57 A 0 0 0.00 0 0.000
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 5 4 1.00 14 0.286
61 A 4 3 1.00 14 0.214
62 A 4 4 1.00 14 0.286
63 A 2 2 1.00 12 0.167
64 A 4 3 1.00 14 0.214
65 A 5 5 1.00 14 0.357
66 A 4 4 1.00 14 0.286
67 A 4 3 1.00 14 0.214
68 A 11 8 1.00 14 0.571
69 A 11 8 1.00 14 0.571
70 A 11 7 1.00 10 0.700
71 A 10 7 1.00 14 0.500
72 A 11 8 1.00 14 0.571
73 A 11 8 1.00 14 0.571
74 A 12 8 1.00 16 0.500
75 A 10 9 1.00 16 0.562
76 A 7 6 1.00 16 0.375
77 A 6 6 1.00 14 0.429
78 A 7 6 1.00 16 0.375
79 A 5 5 1.00 16 0.312
80 A 9 8 1.00 16 0.500
81 A 86 27 1.00 16 1.687
82 A 69 23 1.00 12 1.917
83 A 47 23 1.00 16 1.438
84 A 64 25 1.00 16 1.562
85 A 77 25 1.00 16 1.562
86 A 9 9 1.00 16 0.562
87 A 6 7 1.00 14 0.500
88 A 9 7 1.00 16 0.438
89 A 6 7 1.00 16 0.438
90 A 8 7 1.00 16 0.438
91 A 0 0 0.00 0 0.000
92 A 0 0 0.00 0 0.000
93 A 2 2 1.00 16 0.125
94 A 0 0 0.00 0 0.000
95 A 0 0 0.00 0 0.000
96 A 5 4 1.00 14 0.286
97 A 4 3 1.00 14 0.214
98 A 4 4 1.00 14 0.286
99 A 2 2 1.00 14 0.143
100 A 4 3 1.00 14 0.214
101 A 5 5 1.00 14 0.357
102 A 4 4 1.00 14 0.286
103 A 4 3 1.00 14 0.214
104 A 12 8 1.00 14 0.571
105 A 9 8 1.00 10 0.800
106 A 11 7 1.00 14 0.500
107 A 9 9 1.00 14 0.643
108 A 12 8 1.00 14 0.571
109 A 9 9 1.00 14 0.643
110 A 11 7 1.00 12 0.583
111 A 8 8 1.00 14 0.571
112 A 12 8 1.00 14 0.571
113 A 12 8 1.00 16 0.500
114 A 10 9 1.00 16 0.562
115 A 7 6 1.00 16 0.375
116 A 6 6 1.00 16 0.375
117 A 7 6 1.00 16 0.375
118 A 5 5 1.00 16 0.312
119 A 9 8 1.00 16 0.500
120 A 9 8 1.00 16 0.500
121 A 13 10 1.00 16 0.625
122 A 9 9 1.00 16 0.562
123 A 6 7 1.00 16 0.438
124 A 9 7 1.00 16 0.438
125 A 6 7 1.00 16 0.438
126 A 8 7 1.00 16 0.438
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 2 2 1.00 16 0.125
130 A 0 0 0.00 0 0.000
131 A 0 0 0.00 0 0.000
132 A 5 4 1.00 14 0.286
133 A 5 4 1.00 14 0.286
134 A 4 4 1.00 12 0.333
135 A 4 3 1.00 10 0.300
136 A 4 3 1.00 14 0.214
137 A 2 2 1.00 14 0.143
138 A 4 4 1.00 14 0.286
139 A 5 4 1.00 14 0.286
140 A 14 9 1.00 16 0.562
141 A 9 8 1.00 16 0.500
142 A 9 8 1.00 14 0.571
143 A 6 6 1.00 12 0.500
144 A 7 6 1.00 16 0.375
145 A 6 6 1.00 16 0.375
146 A 7 6 1.00 16 0.375
147 A 17 9 1.00 16 0.562
148 A 15 12 1.00 16 0.750
149 A 8 7 1.00 14 0.500
150 A 6 7 1.00 12 0.583
151 A 9 7 1.00 16 0.438
152 A 6 7 1.00 16 0.438
153 A 9 9 1.00 16 0.562
154 A 6 4 1.00 10 0.400
155 A 5 4 1.00 8 0.500
156 A 4 4 1.00 6 0.667
157 A 4 3 1.00 10 0.300
158 A 4 4 1.00 10 0.400
159 A 5 4 1.00 10 0.400
160 A 3 2 1.00 12 0.167
161 A 3 2 1.00 12 0.167
162 A 2 2 1.00 12 0.167
163 A 4 4 1.00 12 0.333
164 A 3 2 1.00 12 0.167
165 A 4 3 1.00 10 0.300
166 A 4 3 1.00 10 0.300

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